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<meta property="og:description" content="作业5 part 1 1) Give the three representations of an AND gate and say in your words what AND means. 1）Boolean Expression :X = AB
2）Truth Table
   In A IN B Out     0 0 0   0 1 0   1 0 0   1 1 1    3）Logic Diagram Symbol ：
4）AND 是指AB同时为1时结果为1，否则为0
2) Give the three representations of an XOR gate and say in your words what XOR means." />
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<meta property="article:published_time" content="2020-10-07T23:05:44+08:00" />
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<meta name="twitter:description" content="作业5 part 1 1) Give the three representations of an AND gate and say in your words what AND means. 1）Boolean Expression :X = AB
2）Truth Table
   In A IN B Out     0 0 0   0 1 0   1 0 0   1 1 1    3）Logic Diagram Symbol ：
4）AND 是指AB同时为1时结果为1，否则为0
2) Give the three representations of an XOR gate and say in your words what XOR means."/>

  
  
  
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    <h1 id="作业5">作业5</h1>
<h2 id="part-1">part 1</h2>
<h3 id="1-give-the-three-representations-of-an-and-gate-and-say-in-your-words-what-and-means">1) Give the three representations of an AND gate and say in your words what AND means.</h3>
<p>1）Boolean Expression :X = AB</p>
<p>2）Truth Table</p>
<table>
<thead>
<tr>
<th align="center">In A</th>
<th align="center">IN B</th>
<th align="center">Out</th>
</tr>
</thead>
<tbody>
<tr>
<td align="center">0</td>
<td align="center">0</td>
<td align="center">0</td>
</tr>
<tr>
<td align="center">0</td>
<td align="center">1</td>
<td align="center">0</td>
</tr>
<tr>
<td align="center">1</td>
<td align="center">0</td>
<td align="center">0</td>
</tr>
<tr>
<td align="center">1</td>
<td align="center">1</td>
<td align="center">1</td>
</tr>
</tbody>
</table>
<p>3）Logic Diagram Symbol ：</p>
<p><img src="/img/and.png" alt="alt"></p>
<p>4）AND 是指AB同时为1时结果为1，否则为0</p>
<h3 id="2-give-the-three-representations-of-an-xor-gate-and-say-in-your-words-what-xor-means">2) Give the three representations of an XOR gate and say in your words what XOR means.</h3>
<p>1）Boolean Expression :X = A ⊕ B</p>
<p>2）Truth Table</p>
<table>
<thead>
<tr>
<th align="center">In A</th>
<th align="center">IN B</th>
<th align="center">Out</th>
</tr>
</thead>
<tbody>
<tr>
<td align="center">0</td>
<td align="center">0</td>
<td align="center">0</td>
</tr>
<tr>
<td align="center">0</td>
<td align="center">1</td>
<td align="center">1</td>
</tr>
<tr>
<td align="center">1</td>
<td align="center">0</td>
<td align="center">1</td>
</tr>
<tr>
<td align="center">1</td>
<td align="center">1</td>
<td align="center">0</td>
</tr>
</tbody>
</table>
<p>3）Logic Diagram Symbol ：</p>
<p><img src="/img/xor.png" alt="alt"></p>
<p>4）XOR是指AB不同时为1，相同时为0</p>
<h3 id="3-draw-a-circuit-diagram-corresponding-to-the-following-boolean-expression-a--bb--c">3) Draw a circuit diagram corresponding to the following Boolean expression: (A + B)(B + C)</h3>
<p><img src="/img/3.png" alt="alt"></p>
<h3 id="4-show-the-behavior-of-the-following-circuit-with-a-truth-table">4) Show the behavior of the following circuit with a truth table</h3>
<table>
<thead>
<tr>
<th align="center">A</th>
<th align="center">B</th>
<th align="center">A’</th>
<th align="center">AB</th>
<th align="center">A’⊕AB</th>
</tr>
</thead>
<tbody>
<tr>
<td align="center">0</td>
<td align="center">0</td>
<td align="center">1</td>
<td align="center">0</td>
<td align="center">1</td>
</tr>
<tr>
<td align="center">0</td>
<td align="center">1</td>
<td align="center">1</td>
<td align="center">0</td>
<td align="center">1</td>
</tr>
<tr>
<td align="center">1</td>
<td align="center">0</td>
<td align="center">0</td>
<td align="center">0</td>
<td align="center">0</td>
</tr>
<tr>
<td align="center">1</td>
<td align="center">1</td>
<td align="center">0</td>
<td align="center">1</td>
<td align="center">1</td>
</tr>
</tbody>
</table>
<h3 id="5-what-is-circuit-equivalence-use-truth-table-to-prove-the-following-formula-ab--a--b">5) What is circuit equivalence? Use truth table to prove the following formula. (AB)’ = A’ + B’</h3>
<table>
<thead>
<tr>
<th align="center">A</th>
<th align="center">B</th>
<th align="center">A’</th>
<th align="center">B’</th>
<th align="center">AB</th>
<th align="center">(AB)’</th>
<th align="center">A’+B’</th>
</tr>
</thead>
<tbody>
<tr>
<td align="center">0</td>
<td align="center">0</td>
<td align="center">1</td>
<td align="center">1</td>
<td align="center">0</td>
<td align="center">1</td>
<td align="center">1</td>
</tr>
<tr>
<td align="center">0</td>
<td align="center">1</td>
<td align="center">1</td>
<td align="center">0</td>
<td align="center">0</td>
<td align="center">1</td>
<td align="center">1</td>
</tr>
<tr>
<td align="center">1</td>
<td align="center">0</td>
<td align="center">0</td>
<td align="center">1</td>
<td align="center">0</td>
<td align="center">1</td>
<td align="center">1</td>
</tr>
<tr>
<td align="center">1</td>
<td align="center">1</td>
<td align="center">0</td>
<td align="center">0</td>
<td align="center">1</td>
<td align="center">0</td>
<td align="center">0</td>
</tr>
</tbody>
</table>
<h2 id="part-2">part 2</h2>
<h3 id="6-there-are-eight-1bit-full-adder-integrated-circuits-combine-them-to-8bit-adder-circuit-using-the-following-box-diagram">6) There are eight 1bit full adder integrated circuits. Combine them to 8bit adder circuit using the following box diagram.</h3>
<p><img src="/img/4.png" alt="alt"></p>
<h3 id="7-fill-the-follow-expression">7) Fill the follow expression</h3>
<p>(1)  (X8X7X6X5X4X3X2X1)2 or (00001111)2 = ( 0000X2+1 X3+1 X2+1 X1+1 )2</p>
<p>(2)  (X8X7X6X5X4X3X2X1)2 xor (00001111)2 = ( X8⊕⊕0  X7⊕⊕0 X6⊕⊕0 X5⊕⊕0 X4⊕⊕1 X3⊕⊕1 X2⊕⊕1 X1⊕⊕1 )2</p>
<p>(3)  ((X8X7X6X5X4X3X2X1)2 and(11110000)2 ) or  (not (X8X7X6X5X4X3X2X1)2 and (00001111)2)  =  ( X8X7X6X5X4X3X2X1 )2</p>
<h2 id="part-3">part 3</h2>
<h3 id="维基百科解释概念">维基百科解释概念</h3>
<h4 id="1-logic-gate-逻辑门">1) Logic gate 逻辑门</h4>
<p>In electronics, a logic gate is an idealized or physical device implementing a Boolean function; that is, it performs a logical operation on one or more binary inputs and produces a single binary output.<br>
在电子学中，逻辑门是实现布尔函数的理想或物理设备;也就是说，它对一个或多个二进制输入执行逻辑操作，并生成单个二进制输出。</p>
<h4 id="2-boolean-algebra-布尔代数">2) Boolean algebra 布尔代数</h4>
<p>In mathematics and mathematical logic, Boolean algebra is the branch of algebra in which the values of the variables are the truth values true and false, usually denoted 1 and 0 respectively.<br>
在数学和数学逻辑中，布尔代数是代数的一个分支，其中变量的值为真值和假值，通常分别表示为1和0。</p>
<h3 id="自学存储电路">自学存储电路</h3>
<h4 id="1-flip-flop">1) Flip-flop</h4>
<p>中文翻译：触发器</p>
<h2 id="2-sr锁存器">2) SR锁存器</h2>
<p>储存1位二值信号。</p>

  
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